It is known to produce a headrest for a motor vehicle seat, the headrest comprising:                two parallel metal tubular rods for connecting to the seat intended to be mounted at the top of the back of said seat, the rods being in the form of two separate pieces, at least one of the rods being provided with locking detents,        a moulded plastic housing for absorbing energy in the event of impact of a passenger's head on the headrest, the housing being moulded in one piece, the housing comprising two channels in which the rods can slide,        a lining pad of the housing whereon a passenger's head can rest,        two sets of bearings each comprising a top bearing and a bottom bearing, each of the sets being mounted in a corresponding channel by fitting the bearings into receptacles provided in the housing, the receptacles being arranged so as to enable transverse travel of the bearings on either side of a nominal position, the bearings being provided with an opening in which the corresponding rod can slide,        a device for locking the housing relative to the rods in a plurality of vertical positions, so as to enable height adjustment of said pad, the device comprising at least one locking projection movably mounted relative to the housing between a locking position, where the projection is inserted into one of the detents, and an unlocking position, where the projection is removed from the detent so as to release the sliding of the corresponding rod.        
Moulding the housing in one piece makes it possible to limit the risks of rupture of the housing that may be observed when the housing is formed by two half-shells welded to one another.
However, providing two separate rods has various drawbacks:                the mechanical strength of the headrest is not satisfactory insofar as the rods form with the housing three separate pieces subject to micro-movements relative to one another; due to the multiplication of the degrees of freedom, there is a multiplication of the noise sources associated with the vibrations of the various pieces relative to one another,        moreover, proper sliding of the housing on the rods may be impeded due to micro-movements of one rod relative to another potentially creating arching phenomena,        for this reason, such an arrangement requires arranging bearings of significant height, to ensure proper guidance of the rods and counteract the factors of poor sliding mentioned above, which may be incompatible with the space available to house the bearings.        